Statement B correctly negates the universal “all swans are white” by asserting that at least one swan is not white. Statement C is also correct because the negation of “no students are late” is that some students are late. Statement E summarises the general pattern for negating universal statements: replace “all” by “some” and negate the predicate. Statement A is false because “no swans are white” is stronger than the needed negation, and D is false since the negation of “some teachers are not researchers” is “all teachers are researchers”. Therefore, B, C and E only are correct, which matches option B.
Option A:
Option A is incomplete because it omits E (the general rule) and does not include all correct statements needed for the full set.
Option B:
Option B is correct as it combines the proper negations of specific universal and negative statements with the general quantifier rule, while excluding A and D, which overstate or misstate the negations.
Option C:
Option C is wrong because it includes A, which makes the negation of “all swans are white” too strong, so it contains an incorrect statement in the combination.
Option D:
Option D is incorrect since it includes D, which misnegates an existential negative statement, and it omits C, losing one of the correct concrete examples.
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